On the approximation-solvability of equations involving 𝐴-proper and pseudo-𝐴-proper mappings

DOI10.1090/S0002-9904-1975-13728-1zbMath0303.47038MaRDI QIDQ4059490

W. V. Petryshyn

Publication date: 1975

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Equations involving nonlinear operators (general) (47J05) Fixed-point theorems (47H10) Nonlinear elliptic equations (35J60) (Semi-) Fredholm operators; index theories (47A53) Functional equations for functions with more general domains and/or ranges (39B52) Miscellaneous applications of functional analysis (46N99)

Related Items

Controlling the space with preassigned responses ⋮ On the convergence of the collocation method for nonlinear boundary integral equations ⋮ Topological degree and A-proper operators ⋮ On the solvability in Hilbert space of certain nonlinear operator equations depending on parameters ⋮ Remarks on Approximation Methods in Degree Theory ⋮ A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations ⋮ On the boundary element method for some nonlinear boundary value problems ⋮ N-body quantum scattering theory in two Hilbert spaces. IV. Approximate equations ⋮ On the approximation of the linear equations with bounded kernels ⋮ On the galerkln boundary element method for a mixed non-linear boundary value problem ⋮ Some applications of A-proper mappings ⋮ New positive fixed point and eigenvalue results for Pγ-compact maps and some applications ⋮ On the wave operator in few-body quantum scattering with Coulomb-like interactions ⋮ The coupling of boundary integral and finite element methods for nonmonotone nonlinear problems^∗ ⋮ New fixed point theorems for P 1-compact mappings in Banach spaces ⋮ Weak convergence of approximate solutions of stochastic equations with applications to random differential and integral equations^∗ ⋮ The homotopy of certain spaces of nonlinear operators, and its relation to global bifurcation of the fixed points of parametrized condensing operators ⋮ On zeros of semicondensing maps ⋮ A vector parameter global bifurcation result ⋮ Fredholm theory for abstract and differential equations with noncompact nonlinear perturbations of Fredholm maps ⋮ Mappings of accretive and pseudo-A-proper type ⋮ Periodic solutions of semilinear hyperbolic equations at resonance ⋮ Unnamed Item ⋮ Positive solution of a class of equations involving noncompact mappings ⋮ Bifurcation of A-proper mappings without transversality considerations ⋮ Inner approximation-solvability of nonlinear equations ⋮ Role of numerical range in approximation-solvability of nonlinear functional equations ⋮ Constructive proofs of fixed point theorems for set valued operators by simplicial algorithms ⋮ Global results concerning bifurcation for Fredholm maps of index zero with a transversality condition ⋮ Fixed point theorems in probabilistic analysis ⋮ Periodic solutions of certain higher order nonlinear differential equations ⋮ Fredholm alternatives for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems ⋮ Unnamed Item ⋮ Existence theorems for higher order nonlinear periodic boundary value problems ⋮ A generalization of Leray-Schauder theorem and surjectivity results for multivalued A-proper and pseudo A-proper mappings ⋮ A fixed point theorem for a class of differentiable stable operators in Banach spaces ⋮ A generalized-degree homotopy yielding global bifurcation results ⋮ Asymptotically orientation-preserving mappings in Banach spaces ⋮ Existence and uniqueness of initial value problems for a class of second- order differential equations ⋮ Continuation theorems and the approximation-solvability of equations involving multivalued A-proper mappings ⋮ Continuation and surjectivity theorems for uniform limits of A-proper mappings with applications ⋮ An application of A-mapping theory to boundary value problems for ordinary differential equations ⋮ Global bifurcation of a class of periodic boundary-value problems ⋮ Some generalizations of the first Fredholm theorem to multivalued A- proper mappings with applications to nonlinear elliptic equations ⋮ Bifurcation and asymptotic bifurcation for equations involving A-proper mappings with applications to differential equations ⋮ Extension of nonlinear densely defined operators, rates of convergence for the error and the residual, and application to differential equations ⋮ A topological degree of locally A-proper maps ⋮ Semi-numerical Approximation Structures for Nonlinear Noncompact Operators in Banach Spaces ⋮ General approximation-solvability of nonlinear equations involving \(\mathcal A\)-regular operators ⋮ Existence results for equations involving noncompact perturbations of Fredholm mappings with applications to differential equations ⋮ Using degree theory for densely defined A-proper maps in the solvability of semilinear equations with unbounded and noninvertible linear part ⋮ Phi-Stable Operators and Inner Approximation-Solvability ⋮ Solvability of nonlinear perturbations of linear operator equations with parameters ⋮ Galerkin approximations in several parameter bifurcation problems ⋮ The topological degree of A-proper mapping in the Menger PN-space (I) ⋮ A generalized topological degree for S-A-proper mappings and its applications ⋮ The finite difference method for quasilinear elliptic equations of order 2M ⋮ On the collocation method for a nonlinear boundary integral equation ⋮ \(A\)-properness and fixed point theorems for sums of dissipative and ball-condensing maps ⋮ Solvability of Linear and Quasilinear Elliptic Boundary Value Problems via the A-Proper Mapping Theory ⋮ On the Covering Dimension of the Set of Solutions of Some Nonlinear Equations ⋮ Boundary value problems at resonance for certain semilinear ordinary differential equations ⋮ Solvability of Neumann BV problems for nonlinear second-order ODEs which need not be solvable for the highest-order derivative ⋮ Existence theorems for sums of K-ball contractions and accretive operators via A-proper mappings ⋮ Variational solvability of quasilinear elliptic boundary value problems at resonance ⋮ Global bifurcation theory via Galerkin's method ⋮ Periodic solutions of nonlinear second-order differential equations which are not solvable for the highest derivative ⋮ N-body quantum scattering theory in two Hilbert spaces. III. Theory of approximations ⋮ A theorem on A-proper mappings and its application in scattering theory ⋮ \(A\)-properness of contractive and condensing maps ⋮ Higher order nonlinear elliptic equations ⋮ Some further results on periodic solutions of certain higher order nonlinear differential equations

Cites Work

• Normal solvability and 𝜙-accretive mappings of Banach spaces
• Uber die fredholm-alternative bei linearen approximationsregularen operatoren
• The Fixed Point Index of a Differentiable (Β) K -Set Contraction
• On the Fredholm Alternative for Nonlinear Functional Equations in Banach Spaces
• Non-Linear A-Proper Mappings of the Analytic Type
• 𝐴-proper mappings and their uniform limits
• ON A „MONOTONICITY” METHOD FOR THE SOLUTION OF NONLINEAR EQUATIONS IN BANACH SPACES
• A Definition of Degree for Certain Mappings in Hilbert Space
• The radius of the essential spectrum
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monotone (nonlinear) operators in Hilbert space
• Fredholm alternative for nonlinear k-ball-contractive mappings with applications
• Fredholm alternatives for nonlinear A-proper mappings with applications to nonlinear elliptic boundary value problems
• Remarks on nonlinear functional equations. II, III
• Quasi-compact non-linear operators in Banach space and applications
• On a class of K-p.d. and non-K-p.d. operators and operator equations
• On the extension and the solution of nonlinear operator equations
• Fixed point theorems for nonlinear semicontractive mappings in Banach spaces
• On nonlinear P-compact operators in Banach space with applications to constructive fixed-point theorems
• Further remarks on nonlinear P-compact operators in Banach space
• Fixed-point theorems for nonlinear operators and Galerkin approximations
• A fixed point theorem, and some applications
• Méthodes d'approximation et d'itération pour les opérateurs monotones
• On the approximation-solvability of nonlinear equations
• Approximation-solvability of nonlinear functional equations in normed linear spaces
• Remarks on the approximation-solvability of nonlinear functional equations
• Fixed-point theorems involving P-compact, semicontractive, and accretive operators not defined on all of a Banach space
• A Leray-Schauder theorem for a class of nonlinear operators
• Leray-Schauder theorem for P-compact operators and its consequences
• Équations et inéquations non linéaires dans les espaces vectoriels en dualité
• Local boundedness of nonlinear, monotone operators
• Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces
• On projectional-solvability and the Fredholm alternative for equations involving linear A-proper operators
• On nonlinear mappings of strongly semicontractive type
• Fixed points of generalized P-compact operators
• Some examples concerning the distinctive features of bounded linear A-proper mappings and Fredholm mappings
• Functional analysis and Galerkin's method
• Invariance of domain theorem for locally A-proper mappings and its implications
• Surjectivity theorems for odd maps of A-proper type
• Mappings of generalized contractive type
• A generalized degree for uniform limits of A-proper mappings
• Antipodes theorem for A-proper mappings and its applications to mappings of the modified type (S) or (S)+ and to mapping with the pm property
• Nonlinear mappings of analytic type in Banach spaces
• The fixed point index for local condensing maps
• Über die Approximation von linearen Gleichungen zweiter Art und Eigenwertproblemen in Banach-Räumen. (On the approximation of linear equations of second kind and eigenvalue problems in Banach spaces)
• A product formula for the degree of A-proper maps
• Surjectivity results for non-linear mappings from a Banach space to it's dual
• On nonlinear mappings of monotone type homotopic to odd operators
• Noncompact mappings and cones in Banach spaces
• Iterative Lösung gewisser nichtlinearer Operatorgleichungen mit Anwendung auf quasilineare Differentialgleichungen
• On nonlinear equations involving pseudo-A-proper mappings and their uniform limits with applications
• Fixed points of asymptotically linear maps in ordered Banach spaces
• Existence theorems for a class of nonlinear operator equations
• The solvability of non-linear functional equations
• Analytic functional mappings
• Direct and Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space
• On the Structure of the Set of Solutions of Equations Involving A-Proper Mappings
• A Degree Theory, Fixed Point Theorems, and Mapping Theorems for Multivalued Noncompact Mappings
• Fixed Point Theorems for Various Classes of 1-Set-Contractive and 1-Ball- Contractive Mappings in Banach Space
• Topologie et équations fonctionnelles
• Compact analytic mappings of B‐spaces and a theorem of Jane Cronin
• Constructive proofs of representation theorems in separable Hilbert space
• Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder
• MAPPING THEOREMS FOR NONCOMPACT NONLINEAR OPERATORS IN BANACH SPACES
• The closure of the numerical range contains the spectrum
• Constructional Proof of Lax-Milgram lemma and its Application to Non-K-P.D. Abstract and Differential Operator Equations
• On a fixed point theorem for nonlinear $P$-compact operators in Banach space
• A note on d-ideals in some near-algebras
• The topological degree for noncompact nonlinear mappings in Banach spaces
• The topological degree and Galerkin approximations for noncompact operators in Banach spaces
• Semicontractive and semiaccretive nonlinear mappings in Banach spaces
• Fixed-Point Theorems for Certain Classes of Nonexpansive Mappings
• On the Functional Equations Involving Nonlinear Generalized P-Compact Operators
• The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
• Topology and non-linear functional equations
• Fixed Point Theorems for Non-Linear Semicontractive Operators in Banach Spaces
• Iterative Construction of Fixed Points of Contractive Type Mappings in Banach Spaces
• Mapping and Fixed-Point Theorems for Non-Linear Operators in Banach Spaces
• Introduction to the Theory of Bases
• Maximal monotone operators and nonlinear integral equations of Hammerstein type
• Nonlinear elliptic boundary value problems and the generalized topological degree
• On Existence Theorems for Nonlinear Equations Involving Noncompact Mappings
• On the convergence of the Bubnov-Galerkin method
• The Topological Degree of A-Proper Maps
• On the Equivalence of Multiplicity and the Generalized Topological Degree
• Fredholm alternative for nonlinear operators in Banach spaces and its applications to differential and integral equations